Skip to main content
SpringerLink
Log in

An example of non-normal quintic automorphic induction and modularity of symmetric powers of cusp forms of icosahedral type

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Arthur, J., Clozel, L.: Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. Annals of Math. Studies 120. Princeton 1989

  2. Buzzard, K., Dickinson, M., Shepherd-Barron, N., Taylor, R.: On icosahedral Artin representations. Duke Math. J. 109, 283–318 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Buhler, J.: Icosahedral Galois Representations. Springer Lecture Notes 654. Springer 1978

  4. Deligne, P., Serre, J.P.: Formes modulaires de poids 1. Ann. Sci. Éc. Norm. Supér, IV. Sér. 7, 507–530 (1974)

    Google Scholar 

  5. Frobenius, F.G.: Gesammelte Abhandlungen III, Herausgegeben von J.-P. Serre. Springer 1968

  6. Gelbart, S.: Three lectures on the modularity of ρ̄ E,3 and the Langlands reciprocity conjecture. Modular Forms and Fermat’s Last Theorem, pp. 155–204. Springer 1997

  7. Gelbart, S., Jacquet, H.: A relation between automorphic representations of GL(2) and GL(3). Ann. Sci. Éc. Norm. Supér, IV. Sér. 11, 471–552 (1978)

    Google Scholar 

  8. Harris, M.: The local Langlands conjecture for GL(n) over a p-adic field, n<p. Invent. Math. 134, 177–210 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. Harris, M., Taylor, R.: The geometry and cohomology of some simple Shimura varieties. With an appendix by Vladimir G. Berkovich. Annals of Math. Studies 151. Princeton University Press 2001

  10. Henniart, G.: Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique. Invent. Math. 139, 439–455 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Jacquet, H., Langlands, R.P.: Automorphic Forms on GL 2. Lect. Notes Math. 114. Springer 1970

  12. Jacquet, H., Piatetski-Shapiro, I.I., Shalika, J.: Automorphic forms on GL(3), I and II. Ann. Math. 109, 169–212 (1979)

    MATH  Google Scholar 

  13. Jacquet, H., Shalika, J.: Euler products and the classification of automorphic forms I & II. Amer. J. Math. 292, 499–558, 777–815 (1981)

    MathSciNet  Google Scholar 

  14. Kim, H.: Functoriality for the exterior square of GL 4 and symmetric fourth of GL 2. J. Amer. Math. Soc. 16, 139–183 (2002)

    Article  MATH  Google Scholar 

  15. Kim, H., Shahidi, F.: Functorial products for GL 2×GL 3 and symmetric cube for GL 2. Ann. Math. 155, 837–893 (2002)

    MathSciNet  MATH  Google Scholar 

  16. Kim, H., Shahidi, F.: Cuspidality of symmetric powers with applications. Duke Math. J. 112, 177–197 (2002)

    MathSciNet  MATH  Google Scholar 

  17. Langlands, R.P.: Base Change for GL(2). Annals of Math. Studies 96. Princeton 1980

  18. Naimark, M.A., Stern, A.I.: Theory of Group Representations. Grundlehren der Math. Wiss. (English translation) 246. Springer 1980

  19. Ramakrishnan, D.: Modularity of the Rankin–Selberg L–series, and multiplicity one for SL(2). Ann. Math. 152, 45–111 (2000)

    MATH  Google Scholar 

  20. Ramakrishnan, D.: Pure motives and automorphic forms. Motives, Proc. Symp. Pure Math. 55, 411–446 (1994)

    Google Scholar 

  21. Taylor, R.: Icosahedral Galois representations. Pac. J. Math., Olga Taussky-Todd memorial issue (1998)

  22. Taylor, R.: Icosahedral Artin representations II. Amer. J. Math. 125, 549–566 (2003)

    MATH  Google Scholar 

  23. Tunnell, J.: Artin’s conjecture for representations of octahedral type. Bull. Amer. Math. Soc. 5, 173–175 (1981)

    MathSciNet  MATH  Google Scholar 

  24. Wang, S.: On the symmetric powers of cusp forms on GL(2) of icosahedral type. Preprint

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 3G3, Canada

    Henry H. Kim

Authors
  1. Henry H. Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Henry H. Kim.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, H. An example of non-normal quintic automorphic induction and modularity of symmetric powers of cusp forms of icosahedral type. Invent. math. 156, 495–502 (2004). https://doi.org/10.1007/s00222-003-0340-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00222-003-0340-5

Keywords

Search

Navigation